The Size Effect on the Voltage-Dependent Frequency of Fixed-Fixed Carbon Nanotubes Resonator
This work studies the size effect on voltage-dependent resonant frequency of fixed-fixed carbon nanotubes (CNTs) resonator. Specifically, the effect of resonator length, diameter, and gap distance on the variation of the natural frequency under the DC bias voltage is investigated. The resonator is modeled as a cylindrical beam whose ends are ideally fixed on the substrate. Under the condition of neglecting the impact of van der force (gap larger than 100nm), both elastic forces and the electrostatic forces are considered in this study. The variation of frequency with the DC bias voltage is usually decreasing, because the mechanical stiffness is larger than the electrostatic stiffness. But in some case, the effect of the mid-plane stretching dominates that of the electrostatic forcing, and the variation is increasing. Our results shows that the trend of variation is much depend on the size effect of device, especially the size of CNTs diameter. This fact is useful for designers to optimal design of CNTs resonators, either for tunable or stable resonators within a certain range of DC bias voltage.
X. Liao et al., "The Size Effect on the Voltage-Dependent Frequency of Fixed-Fixed Carbon Nanotubes Resonator", Applied Mechanics and Materials, Vols. 66-68, pp. 1245-1250, 2011